Question: Nadia decided to paint some of the rooms at her 19-room inn, Nadia's Place. She discovered she needed $\frac{2}{5}$ of a can of paint per room. If Nadia had 4 cans of paint, how many rooms could she paint?
Solution: We can divide the cans of paint (4) by the paint needed per room ( $\frac{2}{5}$ of a can) to find out how many rooms Nadia could paint. $ \dfrac{{4 \text{ cans of paint}}} {{\dfrac{2}{5} \text{ can per room}}} = {\text{ rooms}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of ${\dfrac{2}{5} \text{ can per room}}$ is ${\dfrac{5}{2} \text{ rooms per can}}$ $ {4\text{ cans of paint}} \times {\dfrac{5}{2} \text{ rooms per can}} = {\text{ rooms}} $ ${\dfrac{20}{2}\text{ rooms}} = 10\text{ rooms}$ Nadia could paint 10 rooms.